The Stability Analysis of a Computer Virus Epidemic Model at disease-free equilibrium

Assumptions of the model

Abstract

In this study, we partitioned the population into Susceptible (S_c), Protected (P_c), Exposed (E_c), Infected (I_c), Quarantined (Q_c) and recovered (R_c) individuals with their corresponding parameters. We analyzed a S_cP_cE_cI_cQ_cR_cS_c compartmental nonlinear deterministic mathematical model of Computer virus epidemic in a community with constant population. Analytical studies were carried out on the model to: investigate the existence and uniqueness of solution of the model equations and explore the basic properties of the model equations (i.e. the positivity and boundedness of solutions of the model). The basic reproductive number  that governs the disease transmission is obtained from the largest eigenvalue of the next-generation matrix. The disease-free equilibrium points of the model is computed and proved to be locally and globally asymptotically stable if  and unstable if  . Finally, we simulate the model system in MATLAB and obtained the graphical behavior of the infected compartmental variables in the model. From the simulation, we observed that the Computer virus infection was eradicated when R₀ < 0while it persist in the environment when R₀ > 0.